# Finding probability

*Suppose it is known that in a certain population 10 percent of the population is color blind. If a random sample of 25 people is drawn from this population, find the probability that 5 or fewer will be color blind.

In solving this problem, what is the significance of the "10 percent"?

• Please add a [self-study] tag and tell us what is your understanding of the problem and where are you stuck?
– Tim
Aug 8, 2018 at 8:48
• Actually, I think I've solved this without considering the "10 percent". In R, I used the code pbinom(q=5,size=25,prob=.5,lower.tail = T) which gave me 0.002038658. So I just wanted to be sure whether my answer is correct without counting the "10 percent" in my calculation. Aug 8, 2018 at 8:58
• How did you arrive to this code? (No, it is not correct.) Please edit your question.
– Tim
Aug 8, 2018 at 9:39
• Are you sure about 0.5 probability? If you draw a sample from a general population and check if individuals are >200 years old, or not, then would the probability be also 0.5 because you could either be >200 y.o. or not?
– Tim
Aug 8, 2018 at 9:54
• Why *0.5 ? I answered below.
– Tim
Aug 8, 2018 at 10:25

You have a population with color blind and non-color blind people. What follows, if you randomly sampled a single person from this population, the probability that you sampled a color-blind person would be $0.1$ (since $10\%$ of the population is color blind), this would be a single Bernoulli trial. If you drew a random sample of size $n$ from this population, then we would be talking $n$ Bernoulli trials, i.e. about binomial distribution with sample size $n$ and probability of "success" $p=0.1$.